Question: Simplify the following expression: $t = \dfrac{7z^2 + 77z + 70}{z + 10} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ t =\dfrac{7(z^2 + 11z + 10)}{z + 10} $ Then we factor the remaining polynomial: $z^2 + {11}z + {10} $ ${10} + {1} = {11}$ ${10} \times {1} = {10}$ $ (z + {10}) (z + {1}) $ This gives us a factored expression: $\dfrac{7(z + {10}) (z + {1})}{z + 10}$ We can divide the numerator and denominator by $(z - 10)$ on condition that $z \neq -10$ Therefore $t = 7(z + 1); z \neq -10$